A man walks 40m North , then 30m East and then 40m South. Find the displacement from the starting point ?

Options

A. 30m East
B. 60m East
C. 30m West
D. 30m West

Answer

To solve the problem, we will analyze the man's movements step by step and calculate the displacement from the starting point.

### Step 1: Understand the movements
1. The man walks **40 m North**.
2. Then he walks **30 m East**.
3. Finally, he walks **40 m South**.

### Step 2: Visualize the movements
- Start at point O (the origin).
- Move **40 m North** to point A.
- From point A, move **30 m East** to point B.
- From point B, move **40 m South** to point C.

### Step 3: Determine the coordinates of each point
- Starting point O (0, 0).
- After moving 40 m North, point A will be (0, 40).
- After moving 30 m East from point A, point B will be (30, 40).
- After moving 40 m South from point B, point C will be (30, 0).

### Step 4: Calculate the displacement
- Displacement is the straight-line distance from the starting point O to the final point C.
- The coordinates of point O are (0, 0) and the coordinates of point C are (30, 0).
- The displacement can be calculated using the formula:

\[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (30, 0) \).

- Plugging in the values:

\[ \text{Displacement} = \sqrt{(30 - 0)^2 + (0 - 0)^2} = \sqrt{30^2} = 30 \text{ m} \]

### Step 5: Direction of the displacement
- The displacement is **30 m towards the East** from the starting point.

### Final Answer
The displacement from the starting point is **30 m East**.

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